The problem considered here is to compare two methods for finding a common boundary between two objects with two unknown geometric parameters, such as edge position and edge orientation. We compare two model-based approaches: the least squares and the minimum Bayesian risk method. An expression is derived for the expected error as a function of radiometry. This shows that the least squares method emphasises outliers. The outliers increase the error in parameter estimation. In an experiment with edge parameter estimation, the negative aspects of least squares are detectable.